Understanding Quantitative Genetics in the Systems Biology Era Mengjin Zhu, Mei Yu, Shuhong Zhao

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International Journal of Biological Sciences 2009; 5(2):161-170 © Ivyspring International Publisher. All rights reserved Review Understanding Quantitative Genetics in the Systems Biology Era Mengjin Zhu, Mei Yu, Shuhong Zhao

Key Laboratory of Agricultural Animal Genetics, Breeding and Reproduction of Ministry of Education, Huazhong Agricul- tural University, Wuhan 430070, P. R. China

Correspondence to: Shuhong Zhao, Key Laboratory of Agricultural Animal Genetics, Breeding and Reproduction of Ministry of Education, Huazhong Agricultural University, Wuhan 430070, P. R. China; Tel: +86-27-87284161; Fax: +86-27-87280408; E-mail: [email protected]

Received: 2008.12.03; Accepted: 2009.01.21; Published: 2009.01.27

Abstract Biology is now entering the new era of systems biology and exerting a growing influence on the future development of various disciplines within life sciences. In early classical and molecular periods of Biology, the theoretical frames of classical and molecular quantitative genetics have been systematically established, respectively. With the new advent of systems biology, there is occurring a paradigm shift in the field of quantitative genetics. Where and how the quantitative genetics would develop after having undergone its classical and molecular periods? This is a difficult question to answer exactly. In this perspective article, the major effort was made to discuss the possible development of quantitative genetics in the systems biology era, and for which there is a high potentiality to develop towards "systems quantitative genetics". In our opinion, the systems quantitative genetics can be defined as a new discipline to address the generalized genetic laws of bioalleles controlling the heritable phenotypes of complex traits following a new dynamic network model. Other issues from quantitative genetic perspective relating to the genetical genomics, the updates of network model, and the future research prospects were also discussed.

Key words: systems quantitative genetics; definition; dynamic network model; prospect

1. Introduction There is a trend in life sciences development that, the advent of systems biology would inevitably give as a discipline, the development of Biology depends explosive birth to a diversity of new fields being on accumulating and assimilating the new knowledge dressed up with a "systems" prefix as the "molecular" in other various disciplines within life sciences, and in in the molecular era. reverse, provides a common time division of their Quantitative genetics was founded, in evolu- historical stages. From Classical Biology to Molecular tionary terms, by the originators of the modern syn- Biology, various life sciences have been led into the thesis. This field is a relatively independent branch of molecular era, e.g., the emergences of the molecular life sciences but the one increasingly applied in a wide biology-related disciplines such as molecular nu- spectrum of scientific disciplines such as evolution, triology, molecular immunology, molecular ecology, animal and plant breeding, behavioral genetics, con- molecular evolution and phylogenetics. Now, the servation biology, medical genetics, ecology, anthro- time has come for Biology to enter the era of systems pology and psychology [4-11], which particularly has biology after having undergone its classical and mo- played a crucial role in relieving the worldwide fam- lecular periods [1-3], which is exerting an increasing ine through genetic improvement of the productivity influence on the transformation of life sciences from a of the agricultural animals and crops. It is anticipated reductionist to a systemic paradigm. It is believed that that new development in quantitative genetics will be

http://www.biolsci.org Int. J. Biol. Sci. 2009, 5 162 of great benefit to various other branches of life sci- and soft inheritance, the genetic information flow ences. An outline of near 100 years' published litera- from DNA polymorphisms to phenotypic variations tures in this field had documented that the historical is not linearly dispersed in living organisms. This de- development of quantitative genetics was rough run- termines that there is no complete congruence be- ning after that of Biology. In its history, the quantita- tween DNA and phenotype. It is very necessary to tive genetics had gone through the first and second open the black box between genes and phenotypes. developmental stages, i.e., the classical and molecular In fact, the phenomena that heritable component quantitative genetics, respectively [12] [13], which, in of phenotypic variation was aroused without DNA despite of having partial overlap, were as expected sequence changes have been proven to have a fre- corresponding to the classical and molecular periods quent occurrence at both cellular and organism levels of Biology. It could be concluded that Biology has also [16-18], which reveal that the variome at the DNA provided the discipline background for the develop- level cannot provide a full elucidation of the heritable ment of quantitative genetics. After the long devel- phenotypes. As suggested by Johannes et al. (2008), opment from classical to molecular quantitative ge- more effort should be given to capture the potentially netics, it might be timely for quantitative genetics to dynamic interplay between chromatin and DNA se- be brought into the third developmental stage in the quence factors in complex traits [19]. There are also coming era of systems biology. many evidences, more accumulated in plants, that non-Mendelian genetic factors modifying the DNA 2. Proposal of systems quantitative genetics can be inherited. On many occasions, quantitative 2.1 Background and definition genetic investigations of target traits only from DNA polymorphisms is no longer absolutely appropriate, Our knowledge of the classical and molecular though it is still debated how important the non-DNA quantitative genetics has undergone a striking expan- sequence variation is in controlling the inheritance of sion in the last century. The classical quantitative ge- phenotypes. Up to date, some pilot work to address netics considers a black box to reveal the holistic this subject has already been undertaken, in which the status of all genes associated with the variation of molecular information mediated between DNA and investigated traits by complicated statistical methods phenotype such as RNA splicing, proteins, metabo- [14]. The subsequently (but partially overlapped in lites or their combinations has been brought into the time) established molecular quantitative genetics new research area of quantitative genetics [20-23]. mainly focuses on evaluating the coupling association How to weigh and integrate the contribution of bio- of the polymorphic DNA sites with the phenotypic logical molecules at different levels and their interac- variations of quantitative and complex traits, as well tions to the heritable component of phenotypes is a as dissecting their genetic architectures, but which new exciting challenge brought to us, of which both never pays attention to the details of how genetic in- classical and molecular quantitative genetics are information is transcriptionally and translationally capable. processed. The absence of the inside functional in- Further development of quantitative genetics formation prevents a definitive identification of the based on the systems biology thinking would provide gene(s) underlying the control of target traits, which an alternative solution to this challenge. Now it is usually requires a subsequent validation of the gene perhaps timely for quantitative genetics to enter into function in more future generations of the same its third developmental stage. Here, as coined by us population or other different populations, or quanti- previously [24], we propose to use the term "Systems tative complementation test. In living organisms, Quantitative Genetics" as the general name of the there are complex genetic and epigenetic mechanisms third generation of quantitative genetics. Aylor and to the molecular regulation of the phenotypic charac- Zeng (2008) have also introduced the concept of sys- teristics of a trait at multiple levels, including DNA tems biology into quantitative genetics, in which a sequence variation, pre- and post- transcription framework was proposed to estimate and interpret events, pre- and post-translation processings, and the epistasis [25], but it involved the gene expression hierarchical or global gene network. It is now well traits rather than the macroscopic phenotype of bio- known that, from DNA to phenotype, the deletion, medically, economically, or evolutionarily important addition, substitution, covalent modification, alterna- traits. In our opinion, the systems quantitative genet- tive packaging of nucleotides, alternative splicing of ics is an interdisciplinary marriage of quantitative mRNAs, and even other kinds of soft inheritance genetics and systems biology. Historically inherited regulations widely participate in the process of han- from the classical and molecular quantitative genetics, dling genetic information [15]. Involving in both hard the systems quantitative genetics, following a new

http://www.biolsci.org Int. J. Biol. Sci. 2009, 5 163 dynamic network model, could be defined as a new fast rate. It appears that the genetical genomics is now discipline that addresses the generalized genetic laws leading the frontier research of quantitative genetics of bioalleles (e.g., DNA sequence alleles, epialleles [29]. Nevertheless, both expressed structural genes [19], transcriptalleles, protealleles, metaboalleles and and eQTLs simultaneously belong to the category of physialleles) underlying the phenotypic variations of gene per se, which is quite different from the conven- interesting traits based on the new thoughts of sys- tional relationship between QTL and the real pheno- tems biology, which is beyond the scope of molecular type in traditional linkage analysis. Such difference quantitative genetics and mainly focuses on parsing results in that the specific regulatory relationships the ab initio mechanism underpinning the relation- between causal loci and the structural genes could be ship between the phenotypes and the analytic status respectively described by two types of eQTLs: cis- and (dynamic network rather than black box or a few trans-eQTL [30] [31]. Actually, the main aim of ge- major genes) of genes in investigated traits.. There are netical genomics is now providing the use for mas- distinct differences among three generations of quan- sively revealing the genetic determinant of the ex- titative genetics (Table 1). pression abundance as well as the derivative characters such as the stability of transcript, the timing of Table 1. Comparisons among classical, molecular and transcription, the alternative splicing [32-35], and the systems quantitative genetics reconstruction of gene regulatory network [36] [37] in Comparative Classical Molecular quan- Systems quantita- various species. items quantitative titative genetics tive genetics genetics From gene expression data to whole-organism Discipline Classical bi- Molecular biol- Systems biology traits, there is an unsolved paradox for genetical ge- background ology ogy nomics (Section 2.2.1). In current, the genetical ge- Depiction of Holistic status Analytical status Analytical status genic system of all genes of major gene of a large set of nomics seems incapable to identify the and holistic genes (and as-yet-undiscovered genes underlying the macro- status of minor downstream genes molecules) scopic phenotypic characteristics and evolutionary Statistical Implicit con- Partially explicit Fully explicit outcomes without other ancillary evidences [38] [39], property sideration for consideration for consideration for all genes major gene and a large set of though in which the "so-called" phenotype -- tran- implicit consid- genes (and script abundance of investigated gene is treated as a eration for minor downstream genes molecules) highly heritable quantitative trait. Entirely unlike this, Phenotypic Static holisti- Static decompo- Dynamic de- the goal of systems quantitative genetics is to unravel property cation of sition of pheno- composition of phenotype type phenotype the ab initio mechanism of the multilevel molecules Variation DNA se- DNA sequence Bioalleles of underlying the heritable phenotypic variations, rather sources to quence alleles alleles and in- molecules at mul- phenotype frequent epial- tiple levels than the mRNA abundance, of organismal traits. leles There is obvious difference in essence between these Model as- Polygenic Major gene plus Gene network two fields. The genetical genomics would therefore sumption model polygene mixed model inheritance not expected to belong to the category of systems model quantitative genetics due to its only concern at the Genetic laws Mendelian Mendelian laws generalized ge- involved laws and partial netic laws in- transcriptional level. A more suitable orientation of non-Mendelian volving in both the genetical genomics in its current status is an ex- laws Mendelian and non-Mendelian tending application of molecular quantitative genetics laws in which the issues of functional genomics, e.g., mas- sive identification of unknown cis regulatory elements 2.2. Beyond the genetical genomics and transcription factors, genetic determinants of Genetical genomics, also colloquially referred to metabolites, and reconstruction of genetic regulatory as "expression genetics", was first introduced by Jan- network, are addressed by the well-established ap- son and Nap [26], and the initial purpose of which proaches or extension methods of molecular quanti- was to provide a powerful paradigm for mapping tative genetics. The principles and techniques of ge- gene expression quantitative trait loci (eQTL) at a netical genomics still fall within the category of the global level [27] [28]. The genetical genomics or eQTL second generation quantitative genetics, though, of is technically a marriage of high-throughput expres- which the algorithms for high dimensional data po- sion profiling technology and quantitative trait loci tentially provides a valuable contribution to the de- (QTL) analysis, but which still holds the underlying velopment of systems quantitative genetics. In our statistical principles of QTL mapping. The body of opinion, as a new discipline, the multilevel-focusing knowledge of this field is growing at an extraordinary systems quantitative genetics is far beyond what the genetical genomics could hold.

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2.2.1. Paradox encountered by genetical genomics genes or QTLs is a precondition to the molecular There have been some researches taking efforts quantitative genetic analyses [48-51]. It could be gen- to identify the undiscovered genes controlling the eralized that the base of quantitative genetics theories organismal traits at tissular, organic, systemic and the logically relies on the hypothesized archetype of entire organism levels by means of gene expression quantitative trait genes, though the formal depictions data [21] [40-44]. However, these researches were of the polygenic and mixed models were not strictly performed under the precondition that either the prior to the shape of some concrete theories in the genes with prior biological functions are involved in developmental history of quantitative genetics. the measurements, or the gene expression measure- The polygenic model takes the whole of the ments are done in specific tissues or cell types with a genes governing target trait(s) as a black box, and of certain biological relevance to target phenotypes [45]. which the holistic properties were roughly depicted Due to the direct or indirect reliance on the prior with several simplifying assumptions [12] [52] [53]. knowledge of the expressed genes, to a certain extent, Consequently, with more understanding of the bio- these investigations led themselves into a circular logical nature of quantitative trait gene, the empirical argument at the philosophic level. Up to date, it is depictions of polygenic model were no longer com- hard to directly confirm that the loci controlling the patible with the known biological reality. It had been expression variation of function-unknown genes also aware that the effect sizes of genes (loci) controlling control the phenotypic variation of macroscopic traits. quantitative traits are not entirely equal, but usually a For the function-known genes, the genetical genomics few major genes and many minor genes are involved just provides a validation rather than an ab initio in most cases. On many occasions, there were mechanistic explanation, and seems to argue in a cir- large-effect genes (loci) that could be statistically de- cle for the purpose of gene discovery. On the other tected [54] [55]. With introduction of application of hand, for the function-unknown genes, it presents molecular biology into quantitative genetics, the linkages between the polymorphic sites and the mixed model had gradually taken shape to modify the mRNA expression traits of function-unknown genes, empirical assumptions of polygenic model in practice which, without other information, remains unsure (Table 2), which, in a simple consideration, was real- whether the polymorphic sites or the expressed genes ized by adding major gene(s) to the polygenic model. are directly associated with the macroscopic pheno- The mixed model made the portrait of quantitative types of interesting traits. There seems a paradox for trait gene was no longer a black box to us, and based genetical genomics to conduct the ab-initio mechanis- on which we can individuate the large-effect genes tic studies that systems quantitative genetics is con- from the polygenic sets. And, theoretically but not cerned with. exactly going after the formal formulation of the mixed model in time order, the subsequent the birth and prosperity of molecular quantitative genetics has 3. From polygenic model to gene network much benefited from such update. However, with model time going on, the mechanistic intuition and an increasingly large volume of knowledge of life sciences 3.1. Historical heritage of quantitative trait gene contradict the assumptions of mixed model as well. It model is now very clear that the characteristics of quantita- There have hitherto been proposed two quanti- tive traits are usually the consequence of the structure tative trait gene (QTG) models to describe the bio- of genetic regulatory networks and the parameters logical archetype of genes underlying quantitative that control the dynamics of those networks [56]. Al- traits: the polygenic model and the major gene plus though paying attention to the difference of gene ef- polygene mixed inheritance model (shortened as fect sizes, the hierarchical rank of genes in mixed mixed model below). From a scientific logic perspec- model is not determined as in polygenic model, which tive, the QTG model provides a basis for the theory essentially exhibits a parallel rather than hierarchical development of quantitative genetics. Most or almost or network relationship of quantitative trait genes. It all of the existed mathematical modelings of quantitative does not reflect the fact. Obviously, in current trait genes were conceptually developed through ex- framework, the assumptions of mixed model also lack tending or transforming the two basic biological an interpretable biological reality and are empirical in models. The former supplies the base for the theorization of nature. It is clear that both polygenic and mixed classical quantitative genetics [12] [46] [47]. The latter models just provide a pseudo- or quasi-archetype of also forms the theoretical basis of molecular quantita- quantitative trait gene. tive genetics because for which the existence of major

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Table 2. Main points of mixed model updated from poly- would take a considerable time, certainly not less than genic model the time that the mixed model have ever taken. Polygenic model Mixed model a 3.2.1. Updated contents of the dynamic network model All variable genes have two Many variable genes have more possible alleles than two alleles in fact • Genes underlying the phenotypic variations of Each contributing gene has Effect size of each contributing gene quantitative and complex traits agree with a hi- small and relatively equal is not entirely equal; there are both effects major and minor genes [57] erarchical/network relationship, which is deci- The allele effects of each gene Besides additive, the allele effects of phered by the four-dimensionalization or dy- are only additive certain genes are also non-additive on some occasions [58] namic tridimensionalization of biological mole- There is no dominance on There are (over-, co-, partial or in- cules (e.g., genes, noncoding RNAs, proteins, each locus complete) dominance loci [59] [60] metabolites and signaling components) via inte- There is no epistasis or inter- There often is epistasis or complex action among different loci interaction among different loci grating the interactions of multiple components contributing to the target trait contributing to the target trait [25] from the data provided by genome-wide [61] [62] The genes are segregating There are linkages between loci mutagenesis libraries, in vivo transcriptional and independently [63-65] epigenetic profiles and other biological molecules Target trait depends solely on The merit of target trait depends on genetics, and environmental genetic and environmental factors profiles during ontogenesis or trait development; influences can be ignored and their interactions [66] [67] • To assess the interindividual and intergroup a So far, there has been a lack of a one-time thorough depiction of variability, the network of quantitative trait genes mixed model. The updates of the mixed model from polygenic one have been gradually solved by separate and fragmentary investi- in different individuals from the same species is gations. topologically homeomorphic at the four-dimensional level, which means that the 3.2. Gene network model: novel modification network topology is four-dimensionally spe- With the biological unreality of the earlier two cies-specific and evolutionarily stable; • QTG models being recognized, it needs an updated Within- and across-generational transfer of net- model or completely new one to adapt the coming work variation follows both Mendelian and development of systems quantitative genetics. Here, non-Mendelian inheritance rules; • according to the viewpoint of systems biology and the Phenotypic scales of target traits can be consid- real biological features of quantitative trait genes, we ered as the accumulated output of the network propose a Gene Network Model (hereafter referred to until the measurement time; • as network model) to update the QTG model (Section Phenotypic variation of quantitative trait can be 3.2.1). described as the disturbance of four-dimensional Unlike the gene regulatory network in functional network induced by the bioalleles of generalized genomics [68] [69], the priority goal of network model genetic factors and their interactions. Systems is to exploit the disturbance principle of gene network quantitative genetic analyses of target traits can under the condition of varying input of both inside be theoretically realized through the measure- and outside factors, as well as the across-generational ments of network parameters; • robustness properties of network output, in which To provide reasonable predictability and con- investigation of variation of network output is far trollability for the complete genetic architectures beyond reconstruction of network architecture. In of target traits, the components on the out- order to achieve the above purpose, the output-constrained nodes or hubs of the gene net- put-constrained elements on the nodes, hubs or work are not particles but "Information Boxes"; modules of quantitative genetic network should be • Disturbance factors affect the phenotypes of tar- treated as analytical objects rather than particles, e.g., get traits completely depending on the network explicit equations or nested functions for formulating characteristics. Under a certain network, the ef- the mutation inside a causal gene. In theory, such fects of both hard and soft inheritance factors on treatment ensures that the event that the mutation target traits are of predictability and controllabil- within a causal gene affects the within- and ity. across-generation behaviors of the gene network is of predictability and controllability, though there cur- 3.3. Compatibility between mixed and network rently still are great challenges and difficulties in the models mathematical solutions. Although the contents of the It is certain that the polygenic and mixed models network model developed by us might be partially or are logistically compatible. There is also a necessity to mainly controversial, we think, a broad consensus assess whether or not it is compatible between the

http://www.biolsci.org Int. J. Biol. Sci. 2009, 5 166 mixed and network models. It can be seen from Fig- which, in our opinion, could be used to alternatively explain ure 1 that a network model could yield a mixed model why too many candidates or QTLs for the same trait had through dimension-reducing mapping, which means been reported but most of which are hitherto unidentifi- that the mixed model is just a special case of the net- able. A. In mixed model, the projected area could be denotative of the effect size of gene. The overlapped projec- work model under the condition of dimen- tion on the surface of the batholith reflects the interlocus sion-reducing simplification. In contrast to the depic- interaction, where the two-time and three-time projection tions of mixed model, the network model is more in overlapping denotes the one-order and two-order inter- accordance with the biological reality, and has a better actions, respectively. For the intralocus interaction (not ability to predict the genetic architectures of target reflected here), considering the diploid organism in which a traits. Obviously, the network model could be gene has two alleles, the interaction can be also expressed downwards compatible with the old mixed model, by the varied projection area of two alleles along with which indicates the network model is a more reason- different combination of alleles. B. In network model, some able and profound model, and can replace the old regulatory links between genes are develop- one. ment-dependent, which dynamically exist at specific developmental stages. The network model is dynamic rather than static.

4. Logical consideration of systems quantitative genetics 4.1. Predictability on the genetic architecture From the standpoint of scientific philosophy, a stronger prediction power is a crucial criterion to ad- just or overturn the old theory to become a new science theory (Kuhn, 1970). As we know, there fre- quently happened the interstudy discrepancy or paradoxical phenomena for major gene identification or QTLs mapping in the same traits. For such di- lemma, except the obscure interpretations such as sampling error and genetic background difference, the molecular quantitative genetics based on the mixed model cannot provide sound explanation or solution. As a major deficiency, the molecular quan- Figure 1. Simplified theoretical machinery of quantitative genetics under network model. In this sim- titative genetics could only provide a passive detec- ple scenario, the tridimensional architecture of genes de- tion of the major genes or QTLs of certain traits under notes the network model and the projection image of genes certain genetic background. It cannot provide active on the surface of the batholith denotes the mixed model. It predictions concerning the status or changes of ge- is easy to understand that the mixed model is just a di- netic architectures of target traits. On the contrary, the mension reduction mapping of the network model. As network model itself declares a network relationship hypothesized in Section 3.2.1, the phenotypic measurement of quantitative trait genes, and once the network equalizes the accumulated output of gene network, and thus model is built up, the output behavior of the network here the batholith supportive of the gene network can be induced by external and/or internal factors can be abstractively expressed as the phenotype. Considering a reliably predicted on its own initiative. In theory, the tridimensional relationship in the network model, the ba- network model could make active prediction on the tholith only receives the direct input information of adja- genetic architectures of target traits under different cent genes, but indirectly the non-adjacent genes act, which genetic background. According to Kuhn, the re- means the effects of non-adjacent genes on the batholith are placement of the mixed model by the network one through the adjacent ones. However, the mixed model takes a bidimensional viewpoint to simplify the gene rela- would be basically in agreement with the basic rule of tionship, in which each gene makes a direct projection on science development. Undoubtedly, based on the the surface of the batholith. Given this, in mixed model, it network model, systems quantitative genetics has a can be inferred that the non-adjacent genes are unavoidable more powerful capability of prediction on the genetic to produce repeated effects on the phenotype (batholith), architectures of target traits.

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4.2. Controllability on the non-additive genetic target traits, the more advanced systems quantitative effects genetics would midwife the birth of a new discipline It is believed that, due to the scientific advance- -- systems breeding that can design an exercisable ment of the network model, the theories of systems scheme to provide a better controllability to perform quantitative genetics would be more advanced than operation on the non-additive genetic effects in future that of earlier generation quantitative genetics, and breeding programs. one aspect of which might be reflected by the bio- 5. Future directions: what issues will be ex- logical explanation and controllable manipulation of non-additive genetic effects. There was a fact that the plored? dominance and epistasis pertaining to non-additive It is expected that there will be more daunting genetic effects were statistically rather than biologi- mathematical challenges for the future development cally described under the theories of classical and of systems quantitative genetics. Nevertheless, the molecular quantitative genetics. As it was historically expectable mathematical difficulties being faced by and is presently utilized, the term interaction has been systems quantitative genetics should not prevent us coined to describe the molecular mechanism of from foreseeing ahead the possible issues, though non-additive genetic effects [70], in which two types even the molecular quantitative genetics is now under of interactions, i.e., intralocus interactions (domi- development during both the peak period of theory nance) and interlocus interactions (epistasis), were researches and the rising period of application re- included. However, the concept interaction in the searches. In our opinion, some of the future researches framework of earlier generation of quantitative ge- in systems quantitative genetics might cover the fol- netics is quite inexplicit, which abstractively makes a lowings: very ambiguous expression without giving distinct (i) Basic conceptual framework of the systems biological definitions of them. In contrast, in the quantitative genetics, including semantic representa- framework of network model, the dominance and tions and the mathematical annotations of termino- epistasis components have a clear mechanistic under- logical systems of new and updated concepts. standing. For instances, Gjuvsland et al. (2007) stated (ii) Theories compendium in this field, consisting that epistasis was one of the generic characteristics of of the theorem's hypotheses, new biological interpre- gene regulatory networks, and presented 19 forms of tations of genetic basis of complex and quantitative interaction modules to embody the biological mean- traits, and the settlement of backward compatibility of ings of epistasis [71], and Omholt et al. (2000) declared the completely new or updated theories to the ear- that the intralocus dominance could be denotative of lier-generational ones, etc. the negative and positive autoregulatory feedback (iii) Model developments for estimating the pa- loops, and the interlocus dominance was intimately rameters that control the dynamics of genetic net- connected to either feedback-mediated epistasis or works, involving in complex and alternatively sim- downstream-mediated epistasis [72]. plified or empirical model designs beyond the tradi- As discussed above, for the ability for providing tional linear models; introduction, development and passive detection rather than active prediction on the realization of higher-dimensional algorithms such as genetic architectures of target traits, the molecular large scale parallel algorithm and composite ma- quantitative genetics is nearly incapable to take com- chine-learning algorithm to break the expectable plete control of the non-additive genetic effects in mathematical difficulties; genetic network recon- current breeding programs. Although so, it could not structions and the corresponding evaluation theories, deny that the non-additive genetic effects are essen- e.g., the intragenerational and intergenerational in- tially controllable. In reality, many research articles heritance rules of Mendelian and non-Mendelian have documented that there exists a widening con- factors under the framework of dynamic network sensus about the evolutionary operability of model, the assembly or conditional combination of the non-additive genetic components [73-80], which, by full-level information from DNA variome to phe- some measures, illuminates the non-additive compo- nome, identification of network components or pa- nents are likely to be favored by natural selection [81] rameters associated with the heritable components and thus there is a real existence of the operability of and noises of target phenotypes; etc. the non-additive genetic components in evolution. It (iv) The promising application topics such as is well known that artificial selection is analogous to, solutions of breeding or evolutionary issues from or even more intense and effective than natural selec- systems quantitative genetic perspective, e.g., estab- tion [82]. Therefore, in theory, due to the powerful lishments of systems breeding and systems evolu- prediction capability to the genetic architectures of tionary theories in biological sense; development and

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